At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 16 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

Answer 1

After t hours,

A is at (-(30+17t),0)
B is at (0,16t)

So the distance d is found by

d^2 = (30+17t)^2 + (16t)^2
= 545t^2 + 1020t + 900
at t=6, d = 163.22

So, now we can find the rate of change for d:

2d dd/dt = 1090t + 1020
2*163.22 dd/dt = 7560
dd/dt = 23.16 knots